Information on Result #696913
Linear OA(3227, 32779, F32, 9) (dual of [32779, 32752, 10]-code), using construction X applied to Ce(8) ⊂ Ce(5) based on
- linear OA(3225, 32768, F32, 9) (dual of [32768, 32743, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(3216, 32768, F32, 6) (dual of [32768, 32752, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(322, 11, F32, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3227, 32779, F32, 2, 9) (dual of [(32779, 2), 65531, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (18, 27, 32779)-net over F32 | [i] | ||
| 3 | Linear OOA(3227, 16389, F32, 2, 9) (dual of [(16389, 2), 32751, 10]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3227, 8194, F32, 9, 9) (dual of [(8194, 9), 73719, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |